The current system of units adopted throughout the entire civilized
world (except those irrational weirdos, the citizens of the United
States of America) was originally formulated by the French (thus
SI which is an abbreviation for Le Système International
d'Unités) and is now commonly called the Metric System.

The standard prefixes used with the Metric System allow us
to conveniently and compactly express both very large and very
small quantities by representing powers of ten. Except for powers
with magnitude less than 3 (10-2,
10-1, 101,
and 102) the prefixes correspond
to powers of ten which are multiples of 3 (103,
10-9, etc.) (In the table below,
the prefixes corresponding to powers of ten which are not multiples
of 3 are shown in red. These are
used less frequently in engineering with the exception of centi-:
the centimeter is a very commonly used unit of length.)

The metric prefixes are meant to be used with units (e.g. milli-meters
or kilo-grams) not with unitless numbers.

Until recently, the standard prefixes only extended to 1018 and 10-18.
As science has marched farther into the huge (the cosmos) and
the tiny (quarks) it has become more common to need extremely
large and small numbers so two new prefixes were invented on each
end of the scale.

Note that the abbreviations for positive powers of ten are
usually capitalized and those for negative powers of ten are usually
in lower case. This prevents confusion between terms like Peta-
and pico, or Mega- and milli-.

In order to talk about numbers (as opposed to writing about
them), we need names for them. I will assume everyone reading
this is familiar with the smaller numbers' names, like seven,
twelve, thousand, and million, as well as combinations like twenty-three
or two hundred seventy-five million forty six thousand one hundred
and eighty four.

Above 999,999,999 (which I'll be durned if I'm going to write
out) things get a bit strange. First of all, there are two primary
naming systems in English, the American and the British. In my
opinion, the American nomenclature stomps all over the British
since it derives directly from the number of zeros in the number.
Also, since I live in the good old US of A, I am familiar with
this system, as are most of my students.

If the number of zeroes are grouped into threes (often indicated
by commas when writing a number using numerals - e.g. 1,000,000)
the prefix in front of "-illion" derives directly from
the Latin terms for the number of groups of three zeroes. Unfortunately,
it has an offset of one group of three. Example: Billion has the
prefix bi- meaning 2. The number one billion (remember, this is
the American system, the British is different) is 1,000,000,000.
Note that there are 2 groups of three zeroes following 1,000.
Trillion (tri- means 3) is 1,000,000,000,000. Tillion has 3 groups
of three after 1,000.

The following table lists all named numbers (or rather names
of numbers equal to 10 raised to an integer power which is a multiple
of three) up to 20 groups of three zeroes following 1,000, plus
the number with 100 such groups. Anyone familiar with Latin can
easily determine the names of all the numbers in between vigintillion
and centillion. (By the way, in Latin, "v" sounds like
the English "w", and the "g" is always "hard"
as in "go".)

Name

Power of 10

Groups of three 0's after 1,000

Million

6

1

Billion

9

2

Trillion

12

3

Quadrillion

15

4

Quintillion

18

5

Sextillion

21

6

Septillion

24

7

Octillion

27

8

Nonillion

30

9

Decillion

33

10

Undecillion

36

11

Duodecillion

39

12

Tredecillion

42

13

Quattuordecillion

45

14

Quindecillion

48

15

Sexdecillion

51

16

Septendecillion

54

17

Octodecillion

57

18

Novemdecillion

60

19

Vigintillion

63

20

Centillion

303

100

In addition, there are a couple of other named large numbers
that do not fit this pattern. First is the Googol,
which is a 1 followed by 100 zeros (10100).
To put this sort of number in perspective, the most recent estimate
(about 1996) I have seen for the number of sub-atomic particles
in the known universe ( in all the billions of galaxies, etc.)
is about 1080! A googol is VERY
big.

Now, if you want to be totally ridiculous, there is the googolplex, which is a 1 followed by a
googol zeroes, in other wordsOne googolplex =
10googol or10 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000!!!GOOD GRIEF!

I do not intend to write a treatise on composing numbers using
Roman Numerals, since their use is limited to a few specialized
contexts, e.g. dates in certain contexts (copyright dates of movies
for instance), page numbers in prefaces to books, etc. If you
really care about how to write 3,799,024 in Roman Numerals and
don't know the rules, you will have to seek elsewhere. If you
know the construction rules, the following will allow you to construct
most reasonable sized (whatever that means) numbers using Roman
Numerals. Roman Numerals may be written in either upper or lower
case letters, but should not use mixed case in one number.